Download A capacitor in an AC circuit

Chapter 17
Electric Charge and Electric Field
Two kinds of charges: positive and
negative
• Two charges of the same kind
REPEL each other
• Two charges of different kinds
ATTRACT each other
Coulomb’s Law
• The magnitude F of the force that each of
two point charges q1 and q2 exerts on each
other when they are separated by a distance
r is directly proportional to the product of
the two charges and inversely proportional
to the distance squared
F = k |q1q2|/r2
Additive forces
r12
q1
r23
q2
r13
q3
ELECTRIC FIELD
GAUSS’s LAW
The total flux ΦE coming out of any closed
surface is proportional to the total electric
charge Qencl inside the volume
surrounded by this surface.
ΦE = Qencl / ɛo
Ɛo = 8.854x10-12C2/(N.m2)
Chapter 18
Electric Potential and Capacitance
ELECTRIC POTENTIAL ENERGY
Electric potential energy is between two
charges (q and q’ ) separated by a distance
r and is defined as:
PE = kqq’/r
Electric potential energy is a scalar and has
units of Joule (J).
When there are more than 2 charges, the total
potential energy is the sum of the energy
associated with each pair of charges
• In the gravitational case, the change in the
potential energy associated with an object
with mass m when moved from the surface
to a height h is
mgh
Similarly, the electric potential energy
associated with a charge q in a field E is:
qEd
When the charge is moved a distance d along
or opposite direction of the field
ELECTRIC POTENTIAL or VOLTAGE
• A charge Q creates an electric field around it.
Similarly, this charge will create an electric potential
V around it, commonly called voltage
It is a scalar and is defined as:
V = kQ/r
The unit for electric potential is the Volt (V).
Consequently, when a charge q is placed at a
distance r from Q, the electric potential energy
between the two charges would be:
U = qV
ELECTRIC POTENTIAL and ELECTRIC FIELD
• For parallel plates separated by a distance d
and a potential difference between them V
the field between the plates is then:
E= V/d
Or
V=Ed
DEFINITION
• The CAPACITANCE C of a capacitor is the
ratio of the magnitude of the charge Q on
either conductor (plate) to the magnitude of
the potential Vab between the conductors
(plates):
C =Q/Vab
The SI unit of capacitance is FARAD
(1farad = 1C/1V)
CAPACITANCE FOR PARALLEL PLATES
• If the capacitor is made of parallel plates
with surface area A and a separation d
between the plates, the capacitance is:
C = ɛ0A/d
Capacitors are often joined
Capacitors are often joined II –
Figures 18.22
Electric Field Energy in a Capacitor
• One of the applications of the capacitor is
to store energy (analogous to the potential
energy stored in a spring)
Ucapacitor = (1/2) CV2
Chapter 19
Current, Resistance, and
Directed-Current Circuits
Current defined
Unit: 1coulomb/second = 1 ampere = 1A
Resistance and Ohm’s Law
• When the potential difference V between the
two ends of a conductor is proportional to
the current I passing through the conductor,
the ratio (V)/(I) is called the resistance of
the conductor :
R = V/I
The SI unit for resistance is the ohm and it is
represented by the Greek letter Ω
1Ω = 1V/A
Resistivity
• The resistance is the property of a given conductor
and it depends on its length L and cross- section
area A
R = ρ L/A
L
ρ characterizes the conduction properties of the
material
Power in Electric Circuit
The power P is defined as
P = VabI
The unit for power is the watt
1W = 1J/s
Power for a pure resistor:
For a pure (single) resistor, we have:
P=VabI
Since V= RI
P = RI2 or P = V2ab/R
Connections in series
Req = R1 + R2 + R3
SAME CURRENT
DIFFERENT POTENTIAL
Connections
in parallel
1/Req = 1/R1 + 1/R2 + 1/R3
SAME POTENTIAL
DIFFERENT CURRENT
Chapter 20
Charges moving with respect to a
field
Charges moving with respect to a
field
Charges moving with respect to a
field
UNIT FOR MAGNETIC FIELD
• The magnetic field B has unit, in SI :
TESLA
1 tesla = 1T=1N/(A.m)
The effect of the sign of a moving
charge
Magnetism and circular motion
F = |q|vB
If the motion is
Circular
F = mv2/R
R = mv/ |q|B
ω = v/R = |q|B/m
Force on a conductor with current
F = ILB
The motor and torque
 = (IaB)bsinΦ
Magnetic field of long straight
conductor
Magnetic field of a long, straight wire:
B = μ0I/(2πr)
r is the distance from the wire
μ0 is called the permeability of vacuum
μ0 = 4π x 10-7 T.m/A
Fields in two conductors side-byside
2 wires with currents flowing in the same direction
attract each other
2 wires with currents flowing in opposite directions
repel each other
F = μ0 L(I1 I2)/(2πr)
Force per unit length
F/L = μ0 (I1 I2)/(2πr)
Currents in a loop
Magnetic field at the center of a circular loop
B = μoI /(2R)
For N loops:
B = μo NI /(2R)
SOLENOID
Magnetic field of a Solenoid: B = μonI
n = number of turns per unit length
n = N/L
Chapter 21
Electromagnetic Induction
Does the field induce a current
or not?
Magnetic flux at various
orientations
Magnetic flux at various
orientations
Magnetic flux at various
orientations
Magnetic flux at various
orientations
•
FRADAY’s
LAW
When the magnetic flux ΦB changes in
time, there is a an induced emf directly
proportional
to the time rate of change of the magnetic flux
:
ɛ = |Δ ΦB /Δt |
If we have a coil with N identical turns, then
ɛ = N |Δ ΦB /Δt |
Lenz’s Law
Lenz’s Law
Self-inductance
Transformers
TRANSFORMERS
V2 / V1 = N2 / N1
If energy completely transformed
V1I1 = V2I2
Energy associated with an
•energy is stored
in an electronic
device.
induced
current.
The R-L circuit
•
The L-C circuit
In this case, the energy is transferred from the electric field
(capacitor) to magnetic field (inductor) and vice versa.
The total energy is however conserved:
The back and forth of the energy constitutes an oscillatory
behavior with a frequency ω:
Chapter 22
Alternating Current
• A coil of wire rotating
with constant angular
velocity in a magnetic
field develops a
sinusoidal oscillating
current.
• The potemtial will vary
from a maximum V at
a frequency ω (or, by a
factor of 2π, as f in
Hz).
What are phasors?
• Phasors are graphic
representations of
location. In two
dimensions, you can
locate a unique point
with a radius vector of
length L and its angle
with respect to zero.
Resistance and Reactance
VR = RI
Resistance and Reactance –
Figure 22.6
Resistance and Reactance –
Figure 22.6
An Inductor in a circuit
VL = XLI
XL = ωL
An Inductor in a circuit
An Inductor in a circuit –
A capacitor in an AC circuit
VC = XCI
XC = 1/ωC
A capacitor in an AC circuit
A capacitor in an AC circuit –
Figure 22.8
The series R-L-C circuit
V=ZI
Current and voltage may be
found
Current and voltage may be
found
Power in AC Circuits
Chapter 23
Electromagnetic Waves
Electromagnetic waves
The electromagnetic wave
The electromagnetic wave
• The waves are transverse: electric to magnetic and both to the
direction of propagation.
•The ratio of electric to magnetic magnitude is
E=cB.
•The wave(s) travel in vacuum at c (speed of light in vaccum).
C = 3.00x108 m/s
•Unlike other mechanical waves, there is no need for a medium
to propagate.
Speed of a wave
vwave = λ /T
vwave = λ f
for light:
c= λ f
S = Ɛ0cE2
S = EB/μo
Sav = (1/2) Ɛ0cE2max
Sav = (EmaxBmax)/(2μ0)
The INTESITY of the wave I :
I = Sav
Reflection and refraction
Refraction
Definition of Index of Refraction
• The index of refraction of an optical material
is
n = c/v
Where c is the speed of light in vacuum and v
the speed of light in the material
The frequency f of the wave does NOT
change when moving from one material to
another
λ =λ0/n
Relation between angles
• The angle of reflection θr is equal to the
angle of incidence θa for al wavelengths
and pair of materials.
• For monochromatic light the angle of
refraction θb is related to the angle of
incidence θa by:
nasin θa = nbsin θb
With the refracted ray being always on
opposite sides of the normal
This is Snell’s Law
To perform calculations, use the
data in Table 23.1
Total internal reflection
Sinθcrit = nb/na
Chapter 24
Geometric Optics
Reflections at a plane surface
Review key terms.
• object
• image
• real
• virtual
• distance to image
• distance to object
• magnification
• upright
• inverted
Sign rules for images and objects
• The position of the object and the
image determine sign convention.
• Object distance:
Object same side of
reflecting/refracting surface as
incoming light: s is positive
image distance:
imaget same side of
reflecting/refracting surface as
outgoing light: s’ is positive
Magnification
m = y’/y = -s’/s
Plane mirrors exhibit left-right
reversal
Have you ever looked at some emergency service vehicles and
wondered what ECILOP or ECNALUBMA means? (Actually it’s
even harder, the letters are reversed in their presentation).
Spherical mirrors
• Reflections from a spherical mirror depend on the
radius of curvature.
1/s + 1/s’ = 2/R
Concave spherical mirrors
Concave spherical mirrors
• Focal length: f
f = R/2
Hence:
1/s + 1/s’ = 1/f
The principal rays for mirror imaging
m = y’/y = -s’/s
The convex spherical mirror
The convex spherical mirror
Reflection and production of
paraxial rays
Specific ray tracing for mirror analysis
Specific ray tracing for mirror
analysis
A complete image construction
A complete image construction
A complete image construction
Refraction at spherical surfaces
(na/s) +(nb/s’) = (nb-na)/R
m = y’/y = -(nas’)/(nbs)
THIN LENSES
The converging lens –
Converging lens
f>0
The principal rays for thin lenses
The converging lens –
Diverging lens
f<0
Diverging lenses and foci
Diverging lenses and foci
The principal rays for thin lenses
Any lens that is THICKER in the center than
the edges is a converging lens with
POSITIVE f
Any lens that is THINNER in the center than
the edges is a diverging lens with
NEGATIVE f
We assume that the index of refraction of the
lens is greater than surrounding one.
Equations for thin lenses
(1/s) + (1/s’) = (n-1)[(1/R1) – (1/R2)]
(1/f) = (n-1)[(1/R1) – (1/R2)]
This is the lensmaker equation
R is positive when it is on the OUTGOING
side (by convention light comes from left)
m = y’/y = -s’/s
Chapter 25
Optical Instruments
The camera
• The shutter controls the exposure time and this depends on the
film (which would be chemistry, the darkening of silver salts on
exposure to light).
• The size of the opening provides interesting physics and is
calibrated as “f-stops”. See page 838 in your text.
• The f-number = focal length/aperture
diameter
f-number = f/D
The intensity is proportional to the square of
the diameter
The projector
The position of the
projector bulb, lens,
and screen image
actually serve as a
“camera in reverse”
The eye
The physics of eyeball optics and the chemistry of rhodopsin’s
conformational changes to produce sight is a masterpiece of
design and function.
Aging changes the focal point of an
eye – Table 25.1
Hyperoptic correction
Myopic correction
• Lenses for correcting vision are described
in terms of power which is defined as the
inverse of the focal length expressed in
meters:
The unit of this “power” is the DIOPTER
Correction for a farsighted person: use s=25 cm
and a converging lens
Correction for a near-sighted person: use s=∞
and a diverging lens
The magnifier
Angular Magnification M:
M = θ’/θ
M=25cm/f(cm)
The microsc
The microsc
Microscope
• m1= -s1’/s1
• M=m1M2 = (25cm)s1’/f1f2